Introduction to trigonometry

Learning Objective:

• we are learning to
  • find missing lengths and angles in right angled triangles
  • distinguish between Pythagoras’ Theorem and trigonometry problems
  • decide whether to use Pythagoras Theorem, sin, cos or tan.

Investing:

• This is useful because it will allow us to find the length of a side or the size of an angle in a right angled triangle

• Historically these techniques were used to draw maps and navigate by the stars - without them we'd have never sailed the oceans
• Sat-nav and mobile devices are programmed with this sort of mathematics to help us navigate today
• Here's a short video clip about using trigonometry in navigation:

• The ideas of trigonometry and Pythagoras' theorem are used every day by engineers and scientists, in contexts such as resolving forces and calculating where projectiles will land.
• Throughout the last few centuries, this has been really important in war when people needed to calculate where munitions (bombs, missiles and mortars) would land.

Preparing:

• You will need to know the key words hypotenuse, opposite and adjacent as applied to the sides of a right-angled triangle
  • the side opposite the right angle is bound to be the longest side and is called the hypotenuse
  • the other side next to the marked angle is the adjacent
  • the side opposite the marked angle is called the opposite

• Checking we're ready:
  • can you identify the different sides of a right-angled triangle with the words 'hypotenuse', 'adjacent' and 'opposite'?
  • use a mini-white-board to show you can...

Pythag and trig which side is which.ppt

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• You will have a deeper understanding if you also know:
  • Pythagoras' Theorem
  • how to calculate a ratio
  • a bit about similar triangles

Discovering:

• Let's start by thinking about a special triangle, an equilateral triangle:
  • Consider an equilateral triangle of side length 10cm.
  • Divide it along one of its lines of symmetry into two congruent right-angled triangles.
  • What angles does the right angled-triangle have in its corners?
  • What length is its shortest side? Why?
  • How can you find the length of the third side of this right angled triangle?
• Can you figure it out yourself from these examples?
• Investigate...

Modeling:

• Here are some examples of people getting it right:

• Here are some examples of people getting it wrong in typical ways: Explain how you know!

• Recall

SOH Sin x = opp/hyp
CAH Cos x = adj/hyp
TOA Tan x = opp/adj
In pairs make you own mnemonic to remember SOH CAH TOA
e.g. Richard of York Gave Battle in Vain - ROYGBIV to remember the conventional 7 colours of the rainbow symbol

Discussing:

In pairs complete the following card match activity with 8 triangles and 16 other cards. Cards include 'dummies' which anticipate common misconceptions such as wrong trig function or the incorrect positioning of data and unknowns.

• What would this one be? Tell your learning partner. Convince them you're right.
• Explain how you know.
• How would you explain this to someone who was new to it?

Extension:

• Write data and unknowns onto blank triangles to match remaining cards from the first task

Plenary:

• Pyramid game from Manga High to consolidate key ideas

http://www.mangahigh.com/en_gb/games/pyramidpanic

Homework:

Explaining:

• One way to do this is...
• Another approach might be...
• A useful shortcut is to...
• This works because...
• It doesn't work when...
• An exception is...
• Watch out for...
• A common mistake is...
• You can check your result by...
• We can prove this works by...

Practicing:

• Some straightforward examples.
• Some harder examples.
• Some mixed examples.
• Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data.
• You can demonstrate fluency by at least...

Sharing:

• A web page or wiki I have created to explain this can be found at...
• A presentation I have created and rehearsed looks like...
• A poster I have drawn or model I have made can be found...

Assessing:

• Check you've mastered this skill by...
• Show you understand by explaining...
• Prove you're an expert in... by...

Developing:

• Next we could learn...
• This leads to...
• Now try...

last edited: Nov 13, 2014 12:36 am